Читать книгу A course of plane geometry - Carlos Alberto Cadavid Moreno - Страница 11

Although this is a book about plane geometry, it only contains very basic results. The most sophisticated results appear in the last chapter, in which many of the propositions of Book I of Euclid’s Elements are proved. For example, you will not find any mention of the Pythagorean theorem. The emphasis is in the rigorous development of the material, following Hilbert’s axiomatic system. Many results are presented which are “intuitively obvious”, and whose proofs are rather involved, pointing out the price one has to pay for deriving everything from the axioms through pure reasoning. In this book you will also learn about plane non-euclidean geometry from the very beginning. This is made possible by the method adopted of thinking of plane geometries as set theoretical structures in which a certain collections of axioms hold.